Thursday, October 10, 2013

Rectifying Raster Data - Rubbersheet

This blogs discusses the transformation methods used to Rubbersheet Raster Images in AutoCAD Raster Design
When rectifying a raster image using the Rubbersheet tool in AutoCAD Raster Design, you can select either Triangular or Polynomial transformation method to transform the raster image. 

Triangular Image Transformation
In the triangular image transformation method, the raster image is divided into triangular regions using the user specified control points. Note that the Denaulay Triangulation method. is used for computing triangulation. Next, transformation is applied to each triangular area.  As a result this method produces much more accurate transformation than the polynomial image transformation method. 

Note that, this method applies transformation to that part of image which is within the area defined by the Denaulays triangulation. The portion of the image laying outside the triangulation is not transformed.  As a result, the Raster Design discards the image data outside the triangulated area which leads to the loss of data. To minimise the loss of data, ensure that the control points are placed as close to the image extents as possible. 

Polynomial Image Transformation
The polynomial image transformation method, transforms the entire images by matching the source and destination points as close as possible. Unlike the triangular transformation method, this method applies transformation on the entire image and therefore does not result in loss of image data. However, this method does not always result in perfectly matched source and destination points. The positional error between the actual destination point (destination point on transformed image) and the destination point specified by the user is given by:

Positional error = √ (∆x + ∆y)

Using this method, you can specify the polynomial degree in the Degree edit box corresponding to the Polynomial radio button. Note that the higher polynomial degree will increase positional accuracy of the image points at the matching locations (source point and destination points), but will increase in warping of the image at locations away from the control points.

To specify a higher polynomial degree you will require to specify a minimum number of control points. The minimum number of  control points for polynomial degrees are as follows:

Polynomial Degrees Minimum Number of Control Points
1 3
2 6
3 10
4 15
5 21